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I. Examples
II. Practice
III. Answer Key
Web Resources
Right Similar Triangles
http://www.mathwarehouse.com/geometry/similar/triangles/geometric-mean.php
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I. Examples
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II. Practice Problems
1) What is the value of x in the triangle below? (Online powerpoint answer)
2) What is the value of x in the triangle below? (Online powerpoint answer)
3) What is the value of x in the triangle below? (Online powerpoint)
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4) What is the value of x in the triangle below? (Online PowerPoint)
5)In the diagram below of right triangle ABC, altitude
BD
is drawn to hypotenuse
AC
,
16AC
, and
7CD
. What is the length of
BD
?
(1)
(2)
74
(3)
(4) 12
6) . The accompanying diagram shows a 24-foot ladder leaning against a building. A
steel brace extends from the ladder to the point where the building meets the ground. The
brace forms a right angle with the ladder.
If the steel brace is connected to the ladder at a point that is 10 feet from the foot of the
ladder, which equation can be used to find the length, x, of the steel brace?
(1)
14
10 x
x
(2)
24
10 x
x
(3)
222
1410 x
(4)
222
2410 x
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7) In the diagram below of right triangle ACB, altitude
CD
intersects
AB
at D. If
3AD
and
4DB
, find the length of in
CD
simplest radical form.
8) The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments
whose lengths are 12 and 48. What is the length of the altitude to the nearest tenth?
9) In the accompanying diagram of
ABC, altitude is drawn to the hypotenuse, separating
the triangle into two smaller triangles, ADC and BDC.
Which statement about these triangles is not always true?
(1) The corresponding angles of all three triangles are congruent.
(2) The corresponding sides of all three triangles are proportional.
(3) The two smaller triangles, ADC and BDC, are congruent.
(4) The two smaller triangles, ADC and BDC, are similar.
10) The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments
whose lengths are 10 and 17. What is the length of the altitude to the nearest hundredth?
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11) In the diagram below of right triangle ACB, altitude
CD
is drawn to hypotenuse
AB
.
If
36AB
and
12AC
, what is the length of
AD
?
12) In the diagram below, the length of the legs
AC
and
BC
of right triangle ABC are 6 cm
and 8 cm, respectively. Altitude
CD
is drawn to the hypotenuse of
ABC
.
What is the length of
AD
to the nearest tenth of a centimeter?
13) In the diagram below,
RST
is a
543
right triangle. The altitude, h, to the
hypotenuse has been drawn. Determine the length of h.
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14) In the diagram below of right triangle ABC,
CD
is the altitude to hypotenuse
AB
,
6CB
, and
5AD
.
What is the length of
BD
15) In the diagram below,
RST
is a
5 12 13
right triangle. The altitude, h, to the
hypotenuse has been drawn. Determine the length of h.
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III. Answer Key
1)
2)
3)
4)
5) (1)
6)
(1)
14
10 x
x
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7)
8) 24
9) (Remember you are looking for the false statement) (3) The two smaller triangles, ADC
and BDC, are congruent.
10) 13.04
11) 4
12) 3.6
13) 2.4
14) 4
15)
3600 60
169 13
h 